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The Weak Weak Category of a Space

Published online by Cambridge University Press:  20 November 2018

C. S. Hoo
C. S. Hoo*
Affiliation:
University of Alberta, Edmonton, Alberta
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Let X be a topological space. We say that cat X ≤ n if there exists a map ϕ: X → T1(X, …, X) such that jϕ≃Δ: X → Xn+1, where T1(X, …, X) is the “fat wedge”, j is the inclusion and Δ is the diagonal map. This is an example of a right structure system. This right structure system leads to an associated weak structure system, namely weak category in this particular case.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 49 - 51
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Berstein, I. and Hilton, P. J., Homomorphisms of homotopy structures. Topologie et géomtrie differentielle, Séminaire Ehresmann, April 1963.Google Scholar
2. Hoo, C. S., Nilpotency class of a map and Stasheff's criterion, Pac. J. Math. 28 (1969), 375-380.Google Scholar
3. Peterson, F. P., Numerical invariants of homotopy type, Colloq. on algebraic topology. Aarhus Universitet (1962), 79-83.Google Scholar